for all \(k\ge 1.\)  Let \(\alpha ^{\ast }\)  and \(N(\alpha )\)  be the conjugate and the
norm of \(\alpha ,\)  respectively. By applying Galois Theorem ([1]}, [2]}), we get
\(\lim _{k\rightarrow \infty }\frac{q_{kH}}{q_{kH-1}}=-\frac{1}{\alpha ^{\ast }}=-\frac{\alpha }{N(\alpha )}:=\beta _{1}. \) 
